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Have a rectangle bdfg with point a on side bd so that ba equals 16 cm and ad equals 8 cm what fraction of the area of the rectangle is inside triangle baf?
ba=(16/(16+8))bd=(16/24)bd=(2/3)bd area of the rectangle = bd*bf area of triangle = (2/3)bd*bf/2=(1/3)*bd*bf 1/3
Why is a over b plus c over d equal ad plus bc divided by bd always valid?
Because it can be derived from a large number of more basic principles applied to numbers. Since a/b and c/d are defined, then b and d are non-zero. Then a/b = ad/bd since multiplying the numerator and denominator of a fraction by a non-zero number leaves it unchanged. Similarly, c/d = bc/bd [These steps implicitly assume the commutative property of multiplication ie there is no difference between premultiplication and postmultiplication] Another property of numbers: If x = p and y = q then x+y = p+q [equals added to equals result in equals]. So a/b + c+d = ad/bd + bc/bd and finally, using the distributive property of multiplication [by 1/bd] over addition, = (ad + bc)/bd Maybe you wish you hadn't asked!
Does distributive property apply to complex numbers?
Yes, for example (a + bi)(c + di) = ac + adi + bic + bidi, and commutative property works as well --> ac + adi + bci + bdi² --> ac + (ad + bc)i + bd(-1) = (ac - bd) + (ad + bc)i
What is a isosceles tetrahedron?
A tetrahedron ABCD is isosceles if AB=BD, AC=BD, and AD=BC. In other words, in an isosceles tetrahedron the opposite edges are equal. See the related link for more information.
How is a plus b over a minus b equals c plus d over c minus d?
(a + b)/(a - b) = (c + d)/(c - d) cross multiply(a + b)(c - d) = (a - b)(c + d)ac - ad + bc - bd = ac + ad - bc - bd-ad + bc = -bc + ad-ad - ad = - bc - bc-2ad = -2bcad = bc that is the product of the means equals the product of the extremesa/b = b/c
